TITLE: Automorphisms of a weighted projective space
QUESTION [23 upvotes]: What is the automorphisms group of the weighted projective space $\mathbb{P}(a_{0},...,a_{n})$ ?
Consider the simplest case of a weighted projective plane, take for instance $\mathbb{P}(2,3,4)$; any automorphism has to fix the two singular points. Consider a smooth point $p\in\mathbb{P}(2,3,4)$. What is the subgroup of the automorphisms of $\mathbb{P}(2,3,4)$ fixing $p$ ?

REPLY [2 votes]: Just to complement Al-Amrani's answer (and to self-promote a little bit): the automorphism 2-group of the weighted weighted projective stack $\mathbb{P}_S(a_1,\ldots,a_n)$ over an arbitrary base scheme $S$ has been computed, and its structure elaborated, in
https://doi.org/10.1016/j.jalgebra.2017.05.002
If I am not misunderstanding something, Al-Amrani's result can be interpreted as saying that the $\pi_0$ of the 2-group of automorphisms of the stack is isomorphic to the group of automorphisms of its coarse moduli space (namely, the corresponding weighted projective space).